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A rectangular coil of $300$ turns has an average area of $25 \mathrm{~cm} \times 10 \mathrm{~cm}$. The coil rotates with a speed of $50 \mathrm{~cps}$ in uniform magnetic field of strength $4 \times 10^{-2} \mathrm{~T}$ about an axis perpendicular to the field. The peak value of the induced emf $($ in $\mathrm{V})$ is
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Verified Answer
The correct answer is:
$30 ~\pi$
Peak value of emf is induced, when longer side of rectangular coil moves perpendicular to the field.
Given,
$$
\begin{aligned}
f &=50 \mathrm{cps}, \\
A &=25 \times 10 \times 10^{-4} \mathrm{~m}^{2} \\
&=250 \times 10^{-4} \mathrm{~m}^{2} \\
B &=4 \times 10^{-2} \mathrm{~T}, \text { and } N=300
\end{aligned}
$$
Peak value of induced emf, $e_{0}=N A B \omega$
$$
\begin{aligned}
&=300 \times 250 \times 10^{-4} \times 4 \times 10^{-2} \times 2 \pi \times 50 \\
&=30 \pi \mathrm{V}
\end{aligned}
$$
Given,
$$
\begin{aligned}
f &=50 \mathrm{cps}, \\
A &=25 \times 10 \times 10^{-4} \mathrm{~m}^{2} \\
&=250 \times 10^{-4} \mathrm{~m}^{2} \\
B &=4 \times 10^{-2} \mathrm{~T}, \text { and } N=300
\end{aligned}
$$
Peak value of induced emf, $e_{0}=N A B \omega$
$$
\begin{aligned}
&=300 \times 250 \times 10^{-4} \times 4 \times 10^{-2} \times 2 \pi \times 50 \\
&=30 \pi \mathrm{V}
\end{aligned}
$$
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